Castaños, Fernando. 1982.
“Elements for a coding system of argumentative acts (part 2)”. Papers on Work in Progress, no. 7. Bologna. Cooperativa Libraria Universitaria Editrice. 15-23.
ELEMENTS FOR A CODING SYSTEM OF ARGUMENTATIVE ACTS’ (part 2)
Fernando Castaños
Institute of Education, University of London
Reference and Predication
Philosophers and semanticists usually distinguish two aspects of reference: definiteness and number. The paradigmatic case which is often studied is reference to a particular or individual, that is, singular definite reference. Other types of reference are contrasted to it. For example, in discussions of aspects of meaning (denotation, sense), reference to an individual is opposed to reference to a class of individuals; then the terms ‘general or “generic’ reference are used. In discussions of logic, reference to an individual is opposed to reference to some and to all individual members of a class; then the terms “plural” and “universal” are used. Sometimes, specially in ontological discussions, reference to an individual is distinguished from reference to a property; then the term “universal” is used, but in a different sense from the previous one. Clearly, how many divisions one wants in the field of reference depends on one’s purposes, and in applied linguistics we will have to decide which ones would be most useful for us.
Different types of predications have also been proposed. Philosophers and semanticists, again, distinguish equatives from non-equatives. But other linguists, mainly grammarians, further subdivide the non-equative sentences into ascriptive and relational ones, i.e. into sentences where a property is predicated of, or ascribed to, an individual or individuals, and sentences where two or more individuals are related. Among the relational sentences, several subcategories can be distinguished, such as comparative and transitive sentences. At present some very interesting attempts to provide a systematic account of relational sentences are being produced within a generative approach, in what 15 sometimes called “case grammar” and sometimes “thematic relations theory”. The frameworks that are emerging seem general enough to deal even with equative and ascriptive sentences.
In some initial attempts to codify academic texts, I have found the need to consider a kind of predication as separate from those mentioned above, and to further subdivide it into several categories. This I have termed inclusions. They are typically but not exclusively, realized by the verb “to be” and an unrestricted noun phrase beginning with an indefinite article (a” or ‘an”). A hierarchical sense relation exists or is established between the head of the noun phrase in the predicate and the subject to which the predicate is applied. The sense relations involved are, for example, superordinate/hyponym, member/group, part/whole, though the latter may present some aspects usually associated with syntagmatic relations and not with hierarchical relations. The reason I have needed to separate this kind of predications is that they seem to lie at the center of certain confusions in coding systems, mainly related to categories such as “classification”, “identification”, “categorization”, “taxonomy”. And the justification for subdividing this kind of predications into several subcategories, depending on the sense relation involved, is that each relation has different logical properties, as will be shown presently.
Having considered reference and predication separately, examples of some combinations follow:
- Reference to particulars
1.1. Singular definite reference
a)Equative predication:
(12) The book is “Wordpower”.
b) Ascriptive predication:
(13) The book is heavy.
1.2. Singular indefinite reference
a) Equative predication:
(14)? A chart is a product. (The sense in which this sentence would be
acceptable beyond doubt would be the inclusive one)
b) Ascriptive predication:
(15) A chart is informative (in the context of another chart not being
informative)
1.3. Plural definite reference
a) Equative predication:
(16) The feathers are the symbols of power.
b) Ascriptive predication:
(17) The feathers are expensive.
1.4. Universal singular (distributive) reference
a) Equative predication:
(18) * Every child is every student. (This “content” would have to be
expressed with two propositions:
(i) Every student is a child, and (ii) Every child is a student.)
b) Ascriptive predication:
(19) Every child is healthy.
1.5. Universal plural reference
a) Equative predication:
(20) * All children are all students. (The situation is like that of (18).)
b) Ascriptive predication:
(21) Al] children are healthy.
2. Generic reference
2.1. Singular:
a) Equative predication:
(22) ‘Man’ is ‘human being’. (Note the need for inverted commas)
b) Ascriptive predication:
(23) Man is rational.
2.2. Plural:
a) Equative predication;
(24) ‘Letters’ are ‘symbols . (Clearly, this non-inclusive sense also
requires inverted commas and would occur in restricted contexts)
b) Ascriptive predication:
(25) Letters are symbolic.
3. Reference to prototypes
a) Equative predication:
(26) A human being is a homo sapiens.
b) Ascriptive predication:
(27) A man is rational.
A few points of interest arise from these combinations. The first thing to note is that from a purely logical point of view, equivalences hold between certain pairs of combinations, such as (19) and (21): here, commitment to “every” implies commitment to “all”, and viceversa. In a similar fashion, the same proposition could be expressed with the following two combinations, if both of them existed: [generic reference-equative predication], [universal reference-equative predication]. But the latter is impossible, as shown in (18). And this is the second thing to note.
The (imaginable) pair of alternative propositional acts that express the same proposition with one member of the pair being possible and the other impossible is probably an extreme case. Impossibility in our examples seems to be associated with psychological difficulty. Perhaps given two alternative realizations of the same proposition, one would be easier to process in certain contexts; in other contexts it would be the other way round, and that is why the two versions are available. Of course, if that is the case, there must also be contexts where the differences, which are rather subtle anyway, are neutralized.
It seems to me, however, that not all the differences can be accounted for in terms of a processing difficulty of the sort hinted at above. Clearly, communicative impact, which at times can even point in the opposite direction, also needs to be taken into account. But there is perhaps a more crucial factor, from the point of view of scientific argumentation. As the philosophical controversy between induction and deduction has shown, only statements about particulars can be tested empirically. As indicated by the inverted commas in the [generic-equative] cases, both the singular and the plural, the role of generic statements would seem to be associated more with discussions within systems of meaning, for their elaboration or modification, than with direct observation of reality based on them.
Having mentioned the points above, which indicate the necessary directions for further research, I wish to consider inclusions, for the reasons already expressed. Three o then will first be examined in syllogism-like reasonings, with the including element being in one of the premises in one occasion and in the conclusion on another; the positions of the included will, of course, be the other way round. After brief comments on those examinations, two more inclusions will be mentioned. The names I have adopted for inclusions are very provisional.
1. Part/whole
(1) Leaf l. is part of plant p.
(2) l has a disease.
(3) p has a disease.
—–
(4) Leaf l is part of plant p
(5) p has a disease
(6) l has a disease.
2. Element of/collective entity.
(1) Flower f is in garden g.
(2) f is red.
(3) g is red.
—–
(4) Flower f is in garden g.
(5) g is green.
(6) f is green.
3. Member of/set
(1) Shoe s is a member of Mary’s wardrobe.
(2) Shoe s is black.
(3) Members of Mary’s wardrobe are black.
(4) Shoe is a member of Mary’s wardrobe,
(5) Members of Mary’s wardrobe are black.
(6) s is black.
The results of the previous examinations can be summarized in the following table:
Part/ Element/ Memeber
Whole collective ent. Set
P(xed) → P(xing) √ ? x
P(xing) → P(xed) x x √
where:
‘P(x)’ means “x has property p”,
‘xed’ stands for “entity included”, and
‘xing’ stands for “entity including”.
There is a big difference between the first two inclusions and the third one, between part/whole and element of/collective entity, on the one hand, and member/set, on the other. In the former case, a statement about the including entity is a statement about a qualitatively different entity than the included elements, about another, larger unit. In the latter case, statements about the including entity are statements about a quantitatively different entity only, about all members of a set, not about the set considered as a unit.
The problem with xed inheriting its properties to xing with xing considered as a unit, is that it depends on very subtle degrees and variable thresholds. For example, it could be said of a garden full of red flowers that it was red, even if the grass were green. But how many flowers are needed before they can inherit their colour to the garden would seem to be a conversational matter.
The difference between the first inclusion, part/whole, and the second, element of/collective entity, seems to be due to which degrees and which thresholds, apply. In other words, the kind of inclusion seems to determine the logic that can be applied,
and when it is applied it operates within conversationally defined limits. But the question arises that the inclusion itself may be variable, that a given xed/xing relation counts as, say, part/whole under some circumstances, and as element of/collective entity under other circumstances. This doubt is increased if we realize that the very adjective used in the second premise also plays a role in determining the logics that can be applied, as will be shown presently.
Set theory formalism avoids the variability of P(xed) → P(xing) reasonings by avoiding the logic of relations like part/whole altogether, as hinted at above in the distinction between qualitative and quantitative inferences. If the need arises to talk about a property of a set considered as a unit, rather than as plurality of members, then that property has to be defined in terms of the properties of its members. That is, the semantics used by set theory is a limited semantics, in that there sense relations do not contain their logic of application, as sense relations do in everyday semantics. The question then arises of whether all discourses can afford to be set theoretical, that is, rigorous but uneconomical in terms of mental effort. But this is an empirical question, which must be left unresolved for the moment.
The fourth inclusion I wish to consider is:
4. Component/compound
(1) Oxygen is a component of water.
(2) Oxygen is heavy.
(3) Water is heavy.
—–
(4) Hydrogen is a component of water.
(5) Water is heavy.
(6) Hydrogen is heavy.
—–
(7) Oxygen is a component of water.
(8) Oxygen is electrically negative.
(9) Water is electrically negative.
Here we see that the component/compound relation is like the part/whole relation for adjectives like ‘heavy’, and is not really a relation, in terms of logical behaviour, for adjectives like ‘electrically negative’. Clearly, knowledge of the world is involved here.
I finally wish to make some brief comments about relations of number systems. There is a sense in which it can be said, and is sometimes said, that the natural numbers are included in the integers, the integers in the fractions, the fractions in the real numbers, and the real numbers in the complex numbers. All elements of the set of natural numbers are also elements of the set of integers, but not all integers are natural numbers. All integers are fractions, but not all fractions are integers. And so on.
Now, the properties of the complex number system are not necessarily shared by the real number system. The real number system does not share all its properties with the fractions. And so on. For example not all statements about subtraction that are true of the natural numbers when considered as elements of the system of integers are true when they are considered as elements of the natural number system only, because not all subtractions which can be carried out between natural-numbers-as-integers can be carried out between natural numbers within the natural number system. Thus, a statement about 3-5 is meaningful if 3 and 5 are seen as integers, but meaningless if they are seen as natural numbers.
The semantic network that emerges is very curious. Looked at from a certain angle, the relationship between natural numbers and integers is hike a hyponym/superordinate relation, like, say, the relationship between dog and ‘mammal’. The two relations could be represented visually in the same way, e.g. with trees. And given an integer, we can say that it is either a natural number or a negative integer (or zero)? but not both at the same time, in the same way that we can say that a mammal is either a dog or a cat (or something else), but not both at the same time.
But looked at from another angle, the relationship is not like a hyponym/superordinate relation. Deductions of the sort: All mammals have warm blood. A dog is a mammal. Therefore, a dog has warm blood” are not necessarily valid for number systems. This would seem to be related to another curious fact. In a taxonomy like the dog/mammal one, the superordinate has less defining features than the hyponym, but in a taxonomy like the natural/integer one, it is the other way round.
The implications of the previous speculations could be important for reading. If when we read, we judge the validity of the inferences in the text on the basis of the semantic networks involved, then familiarity with those networks will make the reading easier, and conversely, familiarity with the inferences will make the construction or modification of the networks easier.
Sense Relations
A few acts constituted by combinations of sense relations in pairs of propositions are presented.
Notation:
‘U’ represents a rhetorical unit
‘p’ represents a proposition
‘P’ represents a predicate
‘x’ represents a referring expression, or subject
‘P(x)’ represents a proposition
‘S’ represents a sentence
‘:’ means “is being used to express”.
— Combination 1:
1. U = S1 + S2 2. S1 : P1(x1) 3. S2 : P1 4. S1 ≠ S2
Example: “That man is Welsh. Welsh is that man.”
Possible name for U: ‘Simple Rephrasing’.
— Combination 2:
1. U = S1 + S2 2. S1 : P1(x1) 3. S2 : P2(x2) 4. P1 and P2 are different but equivalent.
Example: “That man is Welsh. That man is from Wales.”
Possible name for U: ‘Complex Rephrasing’.
— Combination 3:
1. U = S1 + S2 2. S1 : P1(x1) 3. S2 : P2(x2)
4. P2 is a hyponym of P1
Example: “That man is British. That man is Welsh.”
Possible name for U: ‘Precising’.
— Combination 4:
1, 2 and 3 as above 4. P2 is a superordinate of P1
Example: “That man is Welsh.” That man is British.
Possible name for U: ‘Classifying’.
— Combination 5:
1. U = S1 + S2 2. S1 : P1(x1) 3. S2 : P2(x1)
4. P1 and P2 are cohyponyms
Example: “That man is Welsh. That man is Scots.”
Possible name for U: ‘Contradiction’.
— Combination 6:
1, 2 and 4 as above 3. S2 : P2(x2)
Example: same as above
Possible name for U: ‘Contrast’.
In the previous examples the following were varied: a) the relations between the referential expression in S1 and S2, and b) the relations between the predicates in S1 and S2. The variations were systematic, though clearly not comprehensive. The combinations should be taken as an indication of what can be done, and not as a finished product.
1 The first part of this article was published in PWP 6.